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Chapter 8: Problem 50
What is the length of a string that has a standing wave with four nodes (including those at the ends) and \(\lambda=17 \mathrm{cm} ?\)
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What must be the velocity of electrons if their associated wavelength is to equal the radius of the first Bohr orbit of the hydrogen atom?
Describe some of the differences between the orbits of the Bohr atom and the orbitals of the wave mechanical atom. Are there any similarities?
The Lyman series of the hydrogen spectrum can be represented by the equation $$\nu=3.2881 \times 10^{15} \mathrm{s}^{-1}\left(\frac{1}{1^{2}}-\frac{1}{n^{2}}\right)(\text { where } n=2,3, \ldots)$$ (a) Calculate the maximum and minimum wavelength lines, in nanometers, in this series. (b) What value of \(n\) corresponds to a spectral line at 95.0 nm? (c) Is there a line at \(108.5 \mathrm{nm} ?\) Explain.
What is \(\Delta E\) for the transition of an electron from \(n=6\) to \(n=3\) in a Bohr hydrogen atom? What is the frequency of the spectral line produced?
Show that the uncertainty principle is not significant when applied to large objects such as automobiles. Assume that \(m\) is precisely known; assign a reasonable value to either the uncertainty in position or the uncertainty in velocity, and estimate a value of the other.
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